Holdings: Handbook of Weighted Automata

Handbook of Weighted Automata:

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Bibliographic Details
Other Authors:	Droste, Manfred (Editor)
Format:	Electronic eBook
Language:	English
Published:	Berlin [u.a.] Springer 2009
Series:	Monographs in Theoretical Computer Science
Subjects:	Gewichteter Automat Automatentheorie Aufsatzsammlung
Online Access:	BTU01 FHM01 UBG01 UBT01 UBY01 UPA01 Volltext Inhaltsverzeichnis
Physical Description:	1 Online-Ressource (XVII, 608 S.)
ISBN:	9783642014925
DOI:	10.1007/978-3-642-01492-5

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adam_text	CONTENTS PART I FOUNDATIONS CHAPTER 1: SEMIRINGS AND FORMAL POWER SERIES MANFRED DROSTE AND WERNER KUICH 3 1 INTRODUCTION 3 2 MONOIDS AND SEMIRINGS 5 3 FORMAL POWER SERIES 12 4 MATRICES 17 5 CYCLE-FREE LINEAR EQUATIONS 22 REFERENCES 26 CHAPTER 2: FIXED POINT THEORY ZOLTAEN ESIK 29 1 INTRODUCTION 29 2 LEAST FIXED POINTS 30 3 CONWAY THEORIES 38 4 ITERATION THEORIES 41 5 UNIQUE FIXED POINTS 44 6 FIXED POINTS OF LINEAR FUNCTIONS 46 6.1 INDUCTIVE -SEMIRINGS 51 6.2 COMPLETE SEMIRINGS 52 6.3 ITERATIVE SEMIRINGS 53 7 FIXED POINTS OF AFFINE FUNCTIONS 54 7.1 COMPLETE SEMIRING-SEMIMODULE PAIRS 59 7.2 BI-INDUCTIVE SEMIRING-SEMIMODULE PAIRS 61 REFERENCES 62 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/994783361 DIGITALISIERT DURCH XII CONTENTS PART II CONCEPTS OF WEIGHTED RECOGNIZABILITY CHAPTER 3: FINITE AUTOMATA ZOLTDN ESIK AND WERNER KUICH 69 1 INTRODUCTION 69 2 FINITE AUTOMATA OVER SEMIRINGS 70 2.1 FINITE AUTOMATA OVER ARBITRARY POWER SERIES SEMIRINGS 72 2.2 FINITE AUTOMATA OVER CONWAY SEMIRINGS 75 2.3 FINITE LINEAR SYSTEMS 81 3 FINITE AUTOMATA OVER QUEMIRINGS 83 3.1 SEMIRING-SEMIMODULE PAIRS AND QUEMIRINGS 85 3.2 FINITE AUTOMATA OVER QUEMIRINGS AND A KLEENE THEOREM 91 3.3 FINITE LINEAR SYSTEMS OVER QUEMIRINGS 99 REFERENCES 103 CHAPTER 4: RATIONAL AND RECOGNISABLE POWER SERIES JACQUES SAKAROVITCH 105 1 INTRODUCTION 106 2 RATIONAL SERIES AND WEIGHTED RATIONAL EXPRESSIONS 107 2.1 SERIES OVER A GRADED MONOID 107 2.2 RATIONAL SERIES 114 3 WEIGHTED AUTOMATA 122 3.1 THE BEHAVIOUR OF A WEIGHTED AUTOMATON 122 3.2 THE FUNDAMENTAL THEOREM OF AUTOMATA 126 3.3 CONJUGACY AND COVERING OF AUTOMATA 132 4 RECOGNISABLE SERIES AND REPRESENTATIONS 138 4.1 THE FAMILY OF RECOGNISABLE SERIES 138 4.2 OTHER PRODUCTS ON RECOGNISABLE SERIES 141 4.3 SERIES ON A PRODUCT OF MONOIDS 145 5 SERIES OVER A FREE MONOID 151 5.1 THE REPRESENTABILITY THEOREM 152 5.2 REDUCED REPRESENTATIONS 157 5.3 APPLICATIONS OF THE REDUCTION OF REPRESENTATIONS 161 6 SUPPORT OF RATIONAL SERIES 165 7 CONTENTS XIII CHAPTER 5: WEIGHTED AUTOMATA AND WEIGHTED LOGICS MANFRED DROSTE AND PAUL GASTIN 175 1 INTRODUCTION 175 2 MSO-LOGIC AND WEIGHTED AUTOMATA 178 3 WEIGHTED LOGICS 181 4 UNAMBIGUOUS FORMULAS 185 5 DEFINABILITY EQUALS RECOGNIZABILITY 189 6 LOCALLY FINITE SEMIRINGS 194 7 WEIGHTED AUTOMATA ON INFINITE WORDS 197 8 WEIGHTED LOGICS ON INFINITE WORDS 203 9 CONCLUSIONS AND OPEN PROBLEMS 206 REFERENCES 208 CHAPTER 6: WEIGHTED AUTOMATA ALGORITHMS MEHRYAR MOHRI 213 1 INTRODUCTION 214 2 PRELIMINARIES 214 2.1 SEMIRINGS 214 2.2 WEIGHTED TRANSDUCERS AND AUTOMATA 215 3 SHORTEST-DISTANCE ALGORITHMS 217 3.1 ALL-PAIRS SHORTEST-DISTANCE PROBLEMS 218 3.2 SINGLE-SOURCE SHORTEST-DISTANCE PROBLEMS 222 4 RATIONAL OPERATIONS 223 5 ELEMENTARY UNARY OPERATIONS 226 6 FUNDAMENTAL BINARY OPERATIONS 226 6.1 COMPOSITION 226 6.2 INTERSECTION 231 6.3 DIFFERENCE 231 7 OPTIMIZATION ALGORITHMS 233 7.1 EPSILON-REMOVAL 233 7.2 DETERMINIZATION 237 7.3 WEIGHT PUSHING 241 7.4 MINIMIZATION 243 7.5 SYNCHRONIZATION 246 8 CONCLUSION 250 REFERENCES 250 PART III WEIGHTED DISCRETE STRUCTURES CHAPTER 7: ALGEBRAIC SYSTEMS AND PUSHDOWN AUTOMATA ION PETRE AND ARTO SALOMAA : XIV CONTENTS 3.1 DEFINITION AND BASIC REDUCTIONS 261 3.2 INTERCONNECTIONS WITH CONTEXT-FREE GRAMMARS 265 3.3 NORMAL FORMS 267 3.4 THEOREMS OF SHAMIR AND CHOMSKY-SCHUETZENBERGER 271 4 TRANSDUCTIONS 275 5 PUSHDOWN AUTOMATA 279 5.1 PUSHDOWN TRANSITION MATRICES 279 5.2 S^Z 1 »-PUSHDOWN AUTOMATA 281 5.3 EQUIVALENCE WITH ALGEBRAIC SYSTEMS 284 6 OTHER TOPICS 287 REFERENCES 288 CHAPTER 8: LINDENMAYER SYSTEMS JUHA HONKALA 291 1 INTRODUCTION 291 2 ITERATED MORPHISMS AND RATIONAL SERIES 292 3 LINDENMAYERIAN ALGEBRAIC SERIES 296 4 DOL POWER SERIES 302 5 OTHER POWER SERIES GENERALIZATIONS OF L SYSTEMS 307 REFERENCES 309 CHAPTER 9: WEIGHTED TREE AUTOMATA AND TREE TRANSDUCERS ZOLTDN FUELOEP AND HEIKO VOGLER 313 1 INTRODUCTION 314 2 PRELIMINARIES 316 2.1 GENERAL NOTATION 316 2.2 TREES 316 2.3 ALGEBRAIC CONCEPTS 317 2.4 TREE SERIES 320 3 WEIGHTED TREE AUTOMATA 320 3.1 BOTTOM-UP TREE AUTOMATA 320 3.2 RECOGNIZABLE TREE SERIES 321 3.3 CLOSURE PROPERTIES 326 3.4 SUPPORT OF RECOGNIZABLE TREE SERIES 328 3.5 DETERMINIZATION OF WEIGHTED TREE AUTOMATA 330 3.6 PUMPING LEMMATA AND DECIDABILITY 331 3.7 FINITE ALGEBRAIC CHARACTERIZATIONS OF RECOGNIZABLE TREE SERIES. 335 3.8 EQUATIONAL TREE SERIES 342 3. CONTENTS XV 5.2 THE BASIC MODEL 365 5.3 RESTRICTED MODELS 370 5.4 COMPOSITION AND DECOMPOSITION 374 5.5 THE INCLUSION DIAGRAM OF SOME FUNDAMENTAL WTT CLASSES 386 5.6 HIERARCHIES 388 5.7 FURTHER MODELS OF WEIGHTED TREE TRANSDUCERS 391 5.8 FURTHER RESULTS 394 REFERENCES 394 CHAPTER 10: TRACES, SERIES-PARALLEL POSETS, AND PICTURES: A WEIGHTED STUDY INA FICHTNER, DIETRICH KUSKE, AND INGMAR MEINECKE 405 1 INTRODUCTION 406 2 TRACES 407 2.1 WEIGHTED DISTRIBUTED SYSTEMS 407 2.2 OTHER FORMALISMS: PRESENTATIONS, EXPRESSIONS, AND LOGICS 411 2.3 RELATING THE FORMALISMS 413 2.4 HISTORY AND OVERVIEW 421 3 SERIES-PARALLEL POSETS 423 3.1 SERIES-PARALLEL POSETS AND BISEMIRINGS 423 3.2 WEIGHTED BRANDUNG AUTOMATA 425 3.3 RATIONALITY 427 3.4 THE HADAMARD PRODUCT 433 3.5 HISTORY AND OVERVIEW 435 4 PICTURES 436 4.1 PICTURES AND WEIGHTED PICTURE AUTOMATA 436 4.2 OTHER FORMALISMS: EXPRESSIONS AND LOGICS 438 4.3 RELATING THE FORMALISMS 440 4.4 DECIDABILITY ISSUES 444 4.5 HISTORY AND OVERVIEW 445 REFERENCES 446 PART IV APPLICATIONS CHAPTER 11: DIGITAL IMAGE COMPRESSION JUERGEN ALBERT AND JARKKO KARI 453 1 INTRODUCTION 453 2 IMAGE TYPES 454 3 WEIGHTED FINITE AUTOMATA AND MULTI-RESOLUTION IMAGES 457 4 DRAWING WFA IMAGES 459 5 XVI CONTENTS 9 CONCLUSIONS AND OPEN PROBLEMS 476 REFERENCES 477 CHAPTER 12: FUZZY LANGUAGES GEORGE RAHONIS 481 1 INTRODUCTION 481 2 LATTICES AND FUZZY LANGUAGES 483 3 FUZZY RECOGNIZABILITY OVER BOUNDED DISTRIBUTIVE LATTICES 486 3.1 FUZZY RECOGNIZABILITY OVER FINITE WORDS 487 3.2 FUZZY RECOGNIZABILITY OVER INFINITE WORDS 495 3.3 MULTI-VALUED MSO LOGIC 500 4 FUZZY LANGUAGES: AN OVERVIEW 505 4.1 FUZZY LANGUAGES OVER -MONOIDS 506 4.2 FUZZY LANGUAGES OVER RESIDUATED LATTICES 507 4.3 FUZZY AUTOMATA WITH OUTPUTS 509 4.4 FUZZY ABSTRACT FAMILIES OF LANGUAGES 509 4.5 FUZZY TREE LANGUAGES 509 5 APPLICATIONS 510 REFERENCES 513 CHAPTER 13: MODEL CHECKING LINEAR-TIME PROPERTIES OF PROBABILISTIC SYSTEMS CHRISTEL BAIER, MARCUS GROESSER, AND FRANK CIESINSKI 519 1 INTRODUCTION 519 2 MARKOV DECISION PROCESSES 526 3 MAXIMAL REACHABILITY PROBABILITIES 533 4 MODEL CHECKING W-REGULAR PROPERTIES 538 5 PARTIAL ORDER REDUCTION 547 6 PARTIALLY OBSERVABLE MDPS 557 7 CONCLUSION 559 8 APPENDIX 560 REFERENCES 563 CHAPTER 14: APPLICATIONS OF WEIGHTED AUTOMATA IN NATURAL LANGUAGE PROCESSING KEVIN KNIGHT AND JONATHAN MAY 571 1 BACKGROUND 571 2 WFST TECHNIQUES FOR NATURAL LANGUAGE PROCESSING 572 2. CONTENTS XVII 3.5 SUMMARIZATION 586 3.6 OPTICAL CHARACTER RECOGNITION 586 4 APPLICATIONS OF WEIGHTED TREE AUTOMATA 586 4.1 OPEN PROBLEMS 590 5 CONCLUSION 591 REFERENCES 591 INDEX 597
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spelling	Handbook of Weighted Automata Manfred Droste ... (eds.) Berlin [u.a.] Springer 2009 1 Online-Ressource (XVII, 608 S.) txt rdacontent c rdamedia cr rdacarrier Monographs in Theoretical Computer Science Gewichteter Automat (DE-588)7690901-3 gnd rswk-swf Automatentheorie (DE-588)4003953-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Gewichteter Automat (DE-588)7690901-3 s DE-604 Automatentheorie (DE-588)4003953-5 s 1\p DE-604 Droste, Manfred edt Erscheint auch als Druck-Ausgabe, Hardcover 978-3-642-01491-8 https://doi.org/10.1007/978-3-642-01492-5 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018622354&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Handbook of Weighted Automata Gewichteter Automat (DE-588)7690901-3 gnd Automatentheorie (DE-588)4003953-5 gnd
subject_GND	(DE-588)7690901-3 (DE-588)4003953-5 (DE-588)4143413-4
title	Handbook of Weighted Automata
title_auth	Handbook of Weighted Automata
title_exact_search	Handbook of Weighted Automata
title_full	Handbook of Weighted Automata Manfred Droste ... (eds.)
title_fullStr	Handbook of Weighted Automata Manfred Droste ... (eds.)
title_full_unstemmed	Handbook of Weighted Automata Manfred Droste ... (eds.)
title_short	Handbook of Weighted Automata
title_sort	handbook of weighted automata
topic	Gewichteter Automat (DE-588)7690901-3 gnd Automatentheorie (DE-588)4003953-5 gnd
topic_facet	Gewichteter Automat Automatentheorie Aufsatzsammlung
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